Spatial-based Output Feedback Adaptive Feedback Linearization Repetitive Control of Uncertain Rotational Motion Systems Subject to Spatially Periodic Disturbances

In this paper, we propose a new design of spatial-based repetitive control for rotational motion systems required to operate at varying speeds and subject to spatially periodic disturbances. The system has known model structure with uncertain parameters. To synthesize a repetitive controller in spatial domain, a linear time-invariant system is reformulated with respect to a spatial coordinate (e.g., angular displacement), which results in a nonlinear system. A nonlinear state observer is then established for the system. Adaptive feedback linearization is applied to the system with the state observer so as to minimize the tacking error. Moreover, a spatial-based repetitive controller is added and operates in parallel with the adaptively feedback linearized system, which not only further reduces the tracking error but also improves parameter adaptation. The overall output feedback adaptive feedback linearization repetitive control system is robust to structured parameter uncertainty, capable of rejecting spatially periodic disturbances under varying process speeds, and can be proved to be stable and produce bounded tracking error. Finally, feasibility and effectiveness of the proposed scheme is verified by simulation.